Al disociar $n_i$ moles $M_{\nu_+}X_{\nu_-}$ obtenemos:

\begin{equation}
n_+=\nu_+n_i\;\;\;\Rightarrow \;\;\; m_+=\nu_+ m_i
\end{equation}
\begin{equation}
n_-=\nu_- n_i\;\;\;\Rightarrow \;\;\; m_-=\nu_- m_i
\end{equation}

Sustituyendo en la ecuación (61)

\begin{equation}
\mu_i=\mu_{i}^{0}+RTln\left[\gamma_{\pm}^{\nu}\left(\frac{\nu_{+}m_i}{m^0}\right)^{\nu_+}\left(\frac{\nu_-m_i}{m^0}\right)^{\nu_-}\right]
\end{equation}
Agrupando términos
\begin{equation}
\mu_i=\mu_{i}^{0}+RTln\left[\gamma_{\pm}^{\nu}\nu_{\pm}^{\nu}\left(\frac{m_i}{m^0}\right)^{\nu}\right]
\end{equation}
Aplicando propiedades de logaritmos neperianos.
\begin{equation}
\mu_i=\mu_{i}^{0}+\nu RTln\left[\gamma_{\pm}\nu_{\pm}\left(\frac{m_i}{m^{0}}\right)\right]
\end{equation}